In the Hamiltonian form of the equations of motion of a conservative
system with unvarying relations, the kinetic energy is supposed
expressed in terms of the _momenta_ p1, p2, ... and the co-ordinates
q1, q2, ..., as in Sec. 1 (19). Since the symbol [delta] now denotes a
variation extending to the co-ordinates as well as to the momenta, we
must add to the last member of Sec. 1 (21) terms of the types
dP[Tau] dP[Tau]'
------- [delta]q1 + -------- [delta]q1 + ... (1)
dPq1 dPq1
Since the variations [delta]p1, [delta]p2, ... [delta]q1, [delta]q2,
... may be taken to be independent, we infer the equations Sec. 1 (23) as
before, together with
dP[Tau] dP[Tau]' dP[Tau] dP[Tau]'
------ = - --------, ------- = - --------, ..., (2)
dPq1 dPq1 dPq2 dPq2